Packing image and movie strips
Pack image strip to .blend not make sense. 
If you need move project, send it to someone else or to render farm, folow this steps:


create folder for image sequense in folder where your .blend file is  and move/copy your image here. (for better manipulation only)
Link image sequence in your .blend to this images.
Make all paths relative - "Files" - "External Data" - "Make All Paths Relative"


Now you can send your .blend with image sequence folder or move it everywhere and Blender find your image sequence.

Why? because path to images now look like this:

//folder with images/

And not like this:

d:/data/blender/projectxy/folder with images/

In my opinion linking images this way is much more clever way than, make copy and save them direct to .blend file.

PS: work for most render farms - just zip all and send as zip